The present invention relates to medical imaging of the heart, and more particularly, to left ventricle endocardium surface segmentation in medical images.
In many three-dimensional (3D) segmentation problems, it is often required to use a smooth surface mesh to represent the boundary of a segmented object. For example, in left ventricle (LV) endocardium surface segmentation, it is desirable to use a smooth mesh representing the LV endocardium surface to tightly enclose the whole blood pool. Such segmented smooth meshes can be used to extract many useful measures for diagnosis of the LV function, such as the volume, ejection fraction, and myocardium wall thickness. Mesh smoothing is also used in other applications, such as during mesh editing to convert an adjusted rough mesh into a smooth mesh.
In active contour based segmentation methods, smoothness is incorporated in the objective function. However, active contours use little prior knowledge regarding the object being segmented, and the contour often converges to an unrealistic shape. To mitigate this problem, an active shape model (ASM) is used to constrain the deformation of a shape. ASM is not formalized as an optimization problem, but an iterative process is exploited to deform the shape and enforce the shape constraint. During the deformation step, each point of the shape is moved along the normal direction to an optimal position based on certain criteria, such as gradient of the intensity or response of a learning based boundary detector. After this step, a zig-zag shape is achieved. The deformed shape is then projected into a principal components analysis (PCA) subspace, which is learned from training samples. Subspace projection enforces the constrained shape to be similar to the training shapes, and a smooth shape is often achieved using a low dimensional subspace. In K. Li, et al., “Optimal Surface Segmentation in Volumetric Images—A Graph-Theoretic Approach”, IEE Trans. Pattern Anal. Machine Intell., 28(1):119-134, 2006, another method to generate a smooth mesh during mesh deformation based on a graph cut method is proposed. During mesh deformation, a graph is generated, where only smoothing adjustment between neighboring points are allowed. This approach is embedded in a boundary evolution framework. Starting from a smooth mesh, this approach can adjust the boundary and evolve to result in a smooth mesh. However, given an un-smooth mesh, it is not clear how to extend the algorithm to generate a smooth mesh. Unlike the active contour based methods, both ASM and the graph cut based approaches do not explicitly enforce a smoothness measure.
Mesh smoothing can also be explicitly enforced independent of the segmentation algorithms. The simplest approach for smoothing a segmented mesh is the Lapalacian smoothing method, in which a new position for each vertex of the mesh is computed as a weighted average of the current position of the vertex, and its first order neighbors. This process is iterated to smooth the mesh. Typically, Lapalacian smoothing acts as a type of low pass filter, and therefore suffers from a shrinkage problem, in which when the smoothing method is applies iteratively a large number of times, a shape eventually collapses to a point. To alleviate the shrinkage problem, an iterative method consisting of two consecutive Lapalacian smoothing steps can be used. By tuning the parameters in Lapalacian smoothing, a more desirable transfer function of the low pass filter can be designed, for example, a transfer function having a flat passing band and a sharp transition from the passing band to the stop band.
The conventional approaches for mesh smoothing described above, when used in LV endocardium segmentation, do not meet the goal of achieving a smooth mesh that tightly encloses the whole blood pool. For example, the segmented mesh resulting from the conventional mesh smoothing may traverse the blood pool, such that the entire blood pool is not enclosed in the mesh.